Method for tensioning multiple-strand cables

ABSTRACT

A method whereby the strands ( 13,13 A) are fixed one after another between two cable anchors (A,B) integral with the structure. The method consists: in pulling on one of the ends of a strand ( 13 A) from one (A) of the cable anchors, while the other end is fixed on the other cable anchor (B); continuously testing the tensioning condition of the strand ( 13 A), the condition involving in particular the measured values of the strand tension and of a predetermined parameter. The invention is characterized in that the predetermined parameter is the variation of the distance separating the cable anchors (A,B).

[0001] The present invention relates to a method for tensioningmultiple-strand cables.

[0002] Multiple-strand cables can be used in all sorts of civilengineering structures, in particular to support structural members witha long span (bridge decks, stadium roofs) or to stabilize slenderstructures (for example microwave towers).

[0003] Be this as it may, in these types of civil engineeringstructures, it is necessary to tension the strands of a cable so that:

[0004] a) firstly, the total tension in a cable is uniformly distributedbetween all of the component strands, to prevent dangerous excesstensions in some strands, leading in particular to the risk of ruptureby fatigue,

[0005] b) secondly, the tension in the cable as a whole is adjusted to avalue as close as possible to the theoretical value determined when thestructure is designed.

[0006] FR 2 652 866 describes a method of tensioning a multiple-strandcable which ensures a uniform distribution of the tension between all ofthe strands (see item a) above). In this method, the first strand,referred to as a witness strand, is installed and tensioned first, andis then anchored and provided with a measuring cell which indicates thetension in the witness strand at all times during installation of thecable. A second strand is then installed, progressively tensioned, andanchored at the precise moment that the tension in it is equal to thatin the witness strand. The same procedure is followed for the thirdstrand: it is introduced into the cable and then progressively tensioneduntil its tension is equal to that of the witness strand. This processcontinues until the last strand has been tensioned and anchored. Thetension in the witness strand is then released, the measuring cell isremoved, and the witness strand is then tensioned again to the finaltension indicated by the cell.

[0007] Consequently, each time that a new strand is introduced into thecable, its tension is set relative to that of the witness strand; thetwo tensions, which are equal at the time the new strand is anchored,remain equal because they vary in the same manner afterward if therelative position of the cable anchors changes:

[0008] a) either because of a progressive increase in the tension in thecable as the strands are installed,

[0009] b) or because of an external load applied to the structure.

[0010] This method, which is known as the isotension method, thereforeenables all of the strands of a cable to be installed with an a prioriguarantee of uniform distribution of the total force in the cablebetween all the strands.

[0011] It has a number of drawbacks, however.

[0012] First of all, the tensions in the new strand and the witnessstrand remain equal only if the two strands were at the same temperatureat the moment of anchoring the new strand. Experience shows that this isnot always the case: the witness strand is contained in a sheath exposedto sunlight and its temperature can be several tens of degrees higherthan that of the new strand being installed. When the temperatures haveequalized, a relative difference in the values of the tensions in thestrands is then observed, and can exceed 10%. This sometimes requires aretensioning operation, using the method described, to equalize thetensions in the strands, and this represents additional work.

[0013] Moreover, although the prior art method imposes the same tensionin all the strands at the time of installing the cable, the problem ofadjusting a cable in accordance with the specifications imposed by thedesign of the structure remain outside the scope of the prior artmethod.

[0014] One approach that might be envisaged consists of using stiffnesscharacteristics of the structure to which the cable is fixed to computethe tension to be applied to the first strand so that at the end of theinstallation of the strands the tension in the cable reaches a specifictotal. However, experience shows that this approach is imprecise,because of uncertainties as to the real load on the first strand, suchas the real conditions of contact of the sheath, the presence of endtubes temporarily supported by the strand, etc. In practice, thisproblem is overcome by proceeding in two stages:

[0015] the strands are initially installed as previously described at afraction of the final tension (from 60% to 90%, depending on theproject),

[0016] appropriate means are then used to compute the stretch to beimparted to all of the strands to achieve the final tension, thiscomputation yielding reliable results since it is reasonable to assumethat the weight of the sheath is uniformly distributed between all ofthe strands; the calculated stretch is then usually applied to thewitness strand, after which the other strands are retensioned using theisotension method.

[0017] It is obvious that this two-fold process greatly complicates thework and therefore increases the cost associated with installing andadjusting a cable.

[0018] Finally, the prior art method requires the tension in the witnessstrand to be released at the end of the work, followed by demounting themeasuring cell and retensioning the witness strand to the previouslymeasured tension; this also complicates the work.

[0019] An object of the invention is to provide a method of tensioning amultiple strand cable that is free of the drawbacks of the prior arttechnique.

[0020] The invention therefore provides a method of tensioning amultiple strand cable in which said strands are installed one after theother between two cable anchors fastened to the structure, the methodconsisting of:

[0021] pulling on one end of a strand from one of the cable anchors withthe other end fixed to the other cable anchor,

[0022] measuring continuously the value of the tension in the strand,and

[0023] continuously testing a condition for ending tensioning for thestrand, said condition employing an expression that is a function of apredetermined parameter,

[0024] which method is characterized in that said predeterminedparameter is the variation in the distance between said cable anchors.

[0025] Thanks to the above features, it becomes possible:

[0026] to ensure a uniform distribution of the total tension in thecable between all the strands, even if they are at differenttemperatures during installation,

[0027] to impose on the cable as a whole a tension as close as possibleto that specified when the structure is designed, even if the realloading conditions for the structure differ from those allowed for inthe computations for the phase concerned, and

[0028] to eliminate the intermediate stages of retensioning strandsimposed by the prior art technique.

[0029] According to other advantageous features of the invention, themethod further consists in:

[0030] a) determining the theoretical value of the zero tension lengthof the cable as a function of:

[0031] the total number of strands of the cable, the axial stiffness andthe weight per unit length of each of the strands of the cable,

[0032] the theoretical position of the cable anchors as defined by thedrawings of the structure,

[0033] the tension in the cable and the displacements of the cableanchors predicted by the design computations for the structure for apredetermined reference phase occurring after tensioning the cable,

[0034] b) evaluating the initial displacements of the cable anchorsimmediately before installing the first strand of the cable,

[0035] c) during the tensioning of each strand of the cable:

[0036] measuring continuously said distance variation from the step b),

[0037] executing a computation loop to test continuously the conditionfor ending tensioning the strand, using said expression which is afunction of said predetermined parameter, and

[0038] d) locking the strand being tensioned to the cable anchor as soonas the condition for ending tensioning of the strand is satisfied.

[0039] There are essentially two embodiments of a method according tothe invention.

[0040] In a first embodiment: said expression which is a function ofsaid predetermined parameter defines the stretch remaining to be appliedto the strand until the condition for ending tensioning is satisfied.

[0041] In this case, said expression can be defined by the followingparameters:

[0042] i) the stiffness and the weight per unit length of the strand,

[0043] ii) the theoretical zero tension length,

[0044] iii) said initial displacements,

[0045] iv) the tension measured in the strand, and

[0046] v) said distance variation,

[0047] and the strand is locked when the stretch remaining to be appliedis equal to zero.

[0048] It may then be preferable if said expression is also defined by avalue representing the insertion of the keys by which said strand isanchored to its cable anchor.

[0049] In the second embodiment, said expression which is a function ofsaid predetermined parameter can define the locking tension that saidstrand must reach before it can be anchored.

[0050] In this case, said expression is defined by the followingparameters:

[0051] i) the stiffness and the weight per unit length of the strand,

[0052] ii) the theoretical zero tension length,

[0053] iii) said initial displacements,

[0054] iv) said distance variation,

[0055] and the strand is locked when the measured value of the tensionapplied to said strand becomes equal to that of the tension calculatedin this way.

[0056] According to other features of the method applying to bothembodiments as defined above:

[0057] said initial displacements are measured on the structure by aprocedure taking account of the construction tolerances of saidstructure or are determined from the results of design computations forthe structure;

[0058] the cable includes a protective sheath and the method furtherconsists of:

[0059] i) determining the theoretical zero tension length from theweight per unit length of said sheath, and

[0060] ii) during the computation relating to said condition for endingtensioning, increasing the weight per unit length of the strand beingtensioned by a fraction of the weight per unit length of the sheath;

[0061] the method also consists of taking account of the temperature ofthe strand being tensioned during step c) in the computation relating tosaid condition for ending tensioning;

[0062] the method also consists of taking account of the temperatures ofthe cables already installed on the structure and of the structureitself during step b) in the determination of said initialdisplacements.

[0063] Other features and advantages of the present invention willbecome apparent in the course of the following description, which isgiven by way of example only and with reference to the accompanyingdrawings, in which:

[0064]FIG. 1 is a diagram explaining how various concepts used duringthe execution of a tensioning method according to the invention aredefined;

[0065]FIG. 2 is a highly simplified representation of an installationfor tensioning a cable;

[0066]FIG. 3 is a flowchart showing computation steps of a firstembodiment of a method according to the invention;

[0067]FIG. 4 is a flowchart showing computation steps of a secondembodiment of a method according to the invention; and

[0068]FIG. 5 shows one embodiment of apparatus for measuring thevariation in the distance between cable anchors that can be used in amethod according to the invention.

[0069] The following description of a preferred embodiment of a methodaccording to the invention relates to a structure on which cables mustbe installed that takes the form of a suspension bridge whose supporteddeck is constructed by successive cantilevering, a situation in whichthe method is particularly beneficial. Nevertheless, it is expresslyspecified here that the method is not limited to this particularsituation and that any structure involving the installation andtensioning of multiple strand cables may constitute an application of amethod according to the invention.

[0070] The FIG. 1 diagram shows from the side a symmetrical suspensionbridge comprising two pylons 1 and 2 and a deck 3 which rests on piles 4in the lateral spans 5 and 6. In the central span, i.e. between the twopylons, the deck 3 is constructed by successive cantilevering, and thelateral spans 5 and 6 can be constructed in parallel with theconstruction of the central span, using the same technique, orconstructed beforehand, using a different method (on an arch, timedshifting). Be this as it may, and without compromising the generalapplicability of the invention, the examples concern the tensioning of acentral span cable, all the cables anchored to a pylon being installedin a quasi-symmetrical fashion to guarantee the stability of the pylon.The diagram shows a few cables 7, 8, 9, 10 and 11.

[0071] The portion 3A of the central span is deformed by its own weight,by the action of the cables that support it, and by the effect of anysite loads (mobile crews, plant, handling machinery, etc.). Thedeformation is greatly exaggerated in FIG. 1, of course.

[0072] It is assumed that during the next phase of the construction ofthe structure a new cable 12 (not shown in FIG. 1) is to be installedalongside the cable 8 and tensioned using a method according to theinvention.

[0073] The following description of a tensioning method refers to theconcept of “displacement” used by persons skilled in this art. In thiscontext, the “displacement” of a point M of a structure in a given stateis equal to a vector {right arrow over (P₀P)}, where P₀ is the positionof the point M in an original state of the structure and P is theposition of the point M in the state under consideration.

[0074] In the context of computing expressions operative in thecondition for terminating tensioning a strand in a method according tothe invention, any convention can be adopted as to the definition of theorigin of the displacement of a cable anchor; once defined, that originthen applies throughout the computation process.

[0075] The following description of a method according to the inventionalso refers to the concept of the “zero tension length” of a cable orstrand, which theoretically characterizes the tension in an installedcable. The zero tension length L of an installed strand is defined asthe length that that strand would have if it were cut at its cableanchors and measured when held straight with negligible tension. It isbecause the zero tension length L of a cable is less than the straightline distance d between its cable anchors that the cable can develop atension T, which has a vertical component V balancing the weight of thecorresponding section of deck. By judiciously choosing the zero tensionlength of each cable of a structure, the structure is tensioned so thatthe loads on it during construction and in service remain permissible,even if this means repeating the tensioning at certain phases ofconstruction. As already indicated, the strand is tensioned by pullingon its end adjacent the active cable anchor A by means of a jack 15 (seeFIG. 2): any stretching of the strand Δl by the jack produces acorresponding reduction Δl of its zero tension length L.

[0076]FIG. 1 shows some of the basic concepts that apply to theembodiment to be described of a method according to the invention:

[0077] the profile (O) represented in chain-dotted line is the profileof the structure from which the displacements are measured;

[0078] the profile (R_(pr)) represented in full line is the profileassociated with a predetermined reference phase; the reference statedefines the required tension in the cable at the end of the tensioningoperation; at this stage no attempt is made to achieve a given tension,which would then be dependent on site loads, whose intensity andposition cannot be predicted accurately beforehand; to the contrary, thecomputations effected by the computer employed for this purpose seek toimpose a tension in the cable such that if, in the reference state, thecable anchors actually have the displacements predicted by the designcomputations, then the tension in the cable in said reference state isalso that predicted by the design computations. It is important to notethat the values, relating to the reference state, of the tension in thecable and the displacements of the cable anchors taken into account inthe computations, are theoretical values taken directly from the designcomputations, and therefore constitute, as it were, specificationsimposed on the on-site construction work by the designers;

[0079] the profile (I) represented in full line is associated with thephase of measuring the initial displacements of the cable anchors;

[0080] {right arrow over (μ)}A_(pr) is the displacement of the bottomcable anchor A considered in the predetermined reference phase;

[0081] {right arrow over (μ)}A₁ is the initial displacement of the cableanchor A;

[0082] {right arrow over (X)}A₀ is the position vector {right arrow over(OA₀)} of the cable anchor A from which the displacements are measured,O designating the origin of the system of axes Oxyz relative to whichthe structure is described.

[0083] Of course, analogous vectors {right arrow over (μ)}B_(pr), {rightarrow over (μ)}B₁ and {right arrow over (X)}B₀ are assigned to the topcable anchor B.

[0084] From now on the description refers to FIG. 2, which shows thecable 12 in profile during its installation between its two cableanchors A and B, respectively on the deck portion 3A and the pylon 1.The structure of these cable anchors can be that described in the Frenchpatent previously cited. The cable anchor A is that incorporating theanchor jaws or keys by means of which the active end of each strand isattached to the cable anchor. The top cable anchor B is “passive”.

[0085] The cable 12, and all the other cables already installed or yetto be installed, comprise a plurality of strands 13, the number ofwhich, in practice, routinely varies from 30 to 80, for example, andtheir length can be 250 meters or more. Moreover, in the embodimentdescribed, each cable has a protective sheath 14 surrounding all thestrands 13. The sheath 14 is disposed between the cable anchors A and Bat the same time as installing the strand that will be tensioned firstfor the cable concerned, but is not fixed to them. The sheath istherefore threaded over the first strand and all the other strands ofthe same cable are then threaded into the sheath before they areanchored.

[0086] In some structures, however, it is possible to dispense with asheath around the strands provided that they are sufficiently protectedindividually against the risks of corrosion.

[0087] In FIG. 2, four strands 13 have already been installed andtensioned and a fifth strand 15A has been threaded into the sheath 14and anchored to the top cable anchor B and is therefore in the processof being tensioned.

[0088] To this end, a tensioning jack 15 known in the art is mountedtemporarily on the strand 13A. The jack is associated with a sensor 15Afor measuring the traction force that it applies to the strand 13A.

[0089] The device for implementing this method according to theinvention includes, in addition to the jack 15, a microcomputer 16storing in the form of files in a permanent memory 17 all the dataconcerning the cables to be installed on the structure.

[0090] According to the invention, the microcomputer 16 is connected tothe sensor 15A of the jack 15 and also to means for measuring thedistance between the cable anchors A and B adapted to measure thevariation in the distance between them as each strand 13, 13A istensioned. In the situation represented, the measuring means comprise alaser rangefinder 18 fixed to the structure near the cable anchor A anda reflector 19 which reflects the measuring laser beam emitted by therangefinder 18. These rangefinders are well known to the person skilledin the art.

[0091] The microcomputer 16 is also connected to a temperature sensor 20for measuring the temperature of the strand being tensioned. Themicrocomputer 16 is further connected to another sensor 22 whichmeasures the temperature inside a witness cable section 21. This witnesssection, consisting of a bundle of strands and a sheath membersurrounding them, is suspended or otherwise disposed above the deckportion 3A in the vicinity of the cables already installed. This meansthat the temperature inside the sheath of the cables already installedcan be determined without having to pierce the sheath to insert asensor.

[0092] Referring from now on to FIG. 3, the computation algorithm usedby the microcomputer 16 to execute a first embodiment of a methodaccording to the invention using data supplied to it by the tensionsensor 15A, the permanent memory 17, the rangefinder 18 and thetemperature sensor 20 is described. It is assumed that, using anappropriate topographical procedure, it has been possible to measure onsite the effective values of the displacements {right arrow over (μ)}A₁and {right arrow over (μ)}B₁ of the cable anchors, just beforeinstalling the first strand. If this is not the case, it is alwayspossible to use theoretical values of these displacements taken intoaccount in the design process for this phase, provided that thepredicted loading is rigorously respected on site and these values arecorrected by means of a computer, the corrections being necessarybecause the temperatures of the structure and the cables alreadyinstalled generally differ from the theoretical values taken intoaccount during the design computations (whence the benefit in thissituation of the temperature sensor 22).

[0093] In the context of this first embodiment, it is assumed that thecondition for ending tensioning of the strand is expressed by taking asa control parameter the remaining stretch Δl to be applied to thestrand: pulling on the active end of the strand ceases when this stretchbecomes equal to zero.

[0094] However, another embodiment is described hereinafter in which thecontrol parameter is the tension indicated by the sensor 15A; in thiscase, the condition for ending tensioning of the strand is reached whenthe tension in the strand being installed reaches a particular blockingvalue computed by the microcomputer 16 as a function of measurements andstored data.

[0095] Note, however, that the first embodiment has the advantage thatit can take directly into account in the tensioning procedure thesystematic relaxation effect that is a feature of some other deviceswhen the tensioning jack 15 is released, known to persons skilled in theart as “key entry”.

[0096] However, regardless of the method chosen, at the end of thedesign process data is available for computing the theoretical value ofthe zero tension length L_(th) of each cable to be installed. Thecomputation is based on the following data (see FIGS. 3 and 4, step S1):

[0097] the theoretical positions {right arrow over (X)}A₀ and {rightarrow over (X)}B₀ of the cable anchors A and B from which thedisplacements are measured,

[0098] the theoretical values, obtained from the design computations, ofthe tension T_(pr) of the cable and the displacements {right arrow over(μ)}A_(pr) and {right arrow over (μ)}B_(pr) of its cable anchors A and Bfor the predetermined reference phase,

[0099] the axial stiffness EA of the cable, obtained by multiplying thenumber of strands n constituting the cable by the apparent Young'smodulus E of a strand and by the section a of a strand: EA=nEa

[0100] the weight per unit length q of the cable, given by the equationq=q_(g)+nq_(t), q_(g), where q represents the weight per unit length ofthe sheath 14 and q_(t) the unit length of a strand.

[0101] To compute the value of L_(th), it is necessary to solve thefollowing applied mechanics problem: “Given two points A and B in spacewhose relative position is characterized by the vector {right arrow over(AB)}={right arrow over (AB_(pr))}=({right arrow over (X)}B₀+{rightarrow over (μ)}B_(pr))−({right arrow over (X)}A₀+{right arrow over(μ)}A_(pr)), given further a cable of axial stiffness EA and of weightper unit length q, determine the untensioned length L of said cable sothat, once anchored at A and B, it exerts at the point A a force equalto a given value T_(A)”. The classical elastic chain theoretical modelis used to establish the equations needed to solve this problem. Thismodel is described in “Cable Structures” by H. Max Irvine, published in1981 by The MIT Press Series in Structural Mechanics, pages 16 to 20.Symbolically, the theoretical zero tension length L_(th) of the cable isa function of EA, q, {right arrow over (AB)}_(pr) and T_(pr):

L _(th)=Λ(EA, q, {right arrow over (AB)} _(pr) , T _(pr))

[0102] In both embodiments, the method of tensioning a cable begins withthe determination of the initial displacements {right arrow over (μ)}A₁and {right arrow over (μ)}B₁ of the cable anchors (see FIGS. 3 and 4,step S2), which can essentially be obtained in two ways:

[0103] either they are measured on the structure by methods known in theart of geometrical tracking of the pylon 1 and the deck 3A,

[0104] or they are estimated from corresponding theoretical valuesextracted from the design computations and stored in the permanentmemory 17.

[0105] In the latter case, a real load must be imposed on the structurethat is as close as possible to that used in the design computations, inparticular with regard to site loads (plant, lifting machinery, etc.).Moreover, in this case, the raw theoretical values must be corrected totake account of the fact that neither the cables already installed northe remainder of the structure is at the uniform constructiontemperature used in the design computations. The corrective computationis effected by reading a value representative of the temperature of allof the installed cables by means of the sensor 22 and entering anaverage value for the temperature of the remainder of the structure; thecomputer 16 then carries out the necessary computations based on unitarythermal load situations determined during the design computations andstored in the permanent memory 17.

[0106] In the following description, only this first situation isconsidered, and applied to both of the embodiments described.

[0107] Once the initial displacements of the cable anchors have beendetermined in step S2, there follows the threading and tensioning ofeach of the strands of the cable.

[0108] The following operations of the method according to the inventionare executed each time that a strand 13 is tensioned.

[0109] In a first embodiment shown in FIG. 3, during tensioning (forexample of the strand 13A), the computer 16 executes repetitively (instep S3, for example at intervals of one second) a computation todetermine the stretch Δl that remains to apply to the strand 13A beforethe jack 15 is released and the strand 13A is anchored by inserting thekeys into the cable anchor. The data that has to be measured ordetermined on site for this computation comprises:

[0110] the initial displacements {right arrow over (μ)}A₁ and {rightarrow over (μ)}B₁ previously determined (step S2),

[0111] the tension T in the strand measured by means of the sensor 15A,

[0112] the variation Δd of the straight line distance between the cableanchors A and B measured using the rangefinder 18, the origin of Δdbeing taken at the time when the initial displacements are determined,i.e. just before threading the first strand 13,

[0113] the temperature θ_(tor) of the strand 13A measured by the sensor20,

[0114] the insertion of the keys rc.

[0115] As tensioning proceeds, the stretch Δl remaining to be applied tothe strand 13A is displayed on the screen of the microcomputer 16 and asignal can be sent to an automaton 23 controlling the jack 15 to releasethe latter as soon as Δl reaches the value zero, allowing for theinsertion of the keys rc.

[0116] At a given moment in tensioning the strand 13A, its zero tensionlength L is obtained from a function analogous to that used to computethe theoretical length previously described:

L=Λ(Ea, q*, {right arrow over (AB)}, T)

[0117] where:

[0118] Ea is the axial stiffness of the strand,

[0119] q* is the weight per unit length q_(t) of the strand weighted bythe contribution of the strand to supporting the weight per unit lengthq_(g) of the sheath 14:

[0120] q*=q_(t)+q_(g)/i (i is the number of the strand)

[0121] {right arrow over (AB)} represents the relative position of thecable anchors, if they were perfectly installed:

{right arrow over (AB)}=({right arrow over (X)}B ₀+{right arrow over(μ)}B ₁)−({right arrow over (X)}A ₀+{right arrow over (μ)}A ₁)+{rightarrow over (I)}Δd

[0122] where {right arrow over (I)} is the unit vector linking the cableanchors A and B.

[0123] The zero tension length L_(θ), the objective to be achieved atthe end of the tensioning operation, at a temperature θ_(tor), has thevalue:

L _(θ) =L _(th)[1+□(θ_(tor)−θ_(th))]

[0124] where designates the coefficient of expansion of the strand.

[0125] The stretch Δl remaining to be applied to the strand 13A beforereleasing the jack 15 is finally given by the equation:

Δl=L−L _(θ) +rc

[0126] in which rc designates the insertion of the keys (which is of theorder of 4 to 7 mm in practice).

[0127] The strand 13A is then anchored permanently in the cable anchor Aand the jack 15 is detached from it so that it can be used for the nextstrand 13.

[0128] As shown in FIG. 4, in a second embodiment of the invention,steps S1 and S2 are executed in the same way as in the first embodiment.

[0129] The second embodiment differs in the step S3, during which,instead of computing the stretch value Δl, a value T is computedrepresenting the locking tension to be achieved in the strand 13A beforeanchoring can take place.

[0130] The locking tension T_(bloc) is determined from the values {rightarrow over (AB)}, q* and L_(θ) using the following equation:

T _(bloc) =T(Ea,q*,{right arrow over (AB)},L _(θ)

[0131] Note that the determination of the function T above can use thesame elastic chain theory as described in the work previously cited, theproblem to be solved being based on looking for the value T rather thanthe value of L.

[0132] The value of the locking tension T_(bloc) computed by thecomputer 16 is displayed in a window V2 of the screen and the real valueof the tension in the strand 13A measured by means of the sensor 15A isdisplayed simultaneously in another window V1. Locking is effected assoon as the values in the windows V1 and V2 are equal. The process canbe stopped automatically by the automaton 23 as soon as the condition ofequality applies.

[0133]FIG. 5 shows a variant of the rangefinder 18A for measuring thevariation of the distance between the cable anchors A and B and whichcan also be used to execute the method according to the invention. Inthis case, an Invar® wire, for example, is fixed at one end to the pylon1 in the vicinity of the top cable anchor B. The other end of the wirepasses over a pulley 24 mounted in the vicinity of the bottom cableanchor A and is attached to a weight 25. An electronic comparator 26 onthe portion 3A of the deck under construction measures the variation ofthe vertical position of the weight 25 in order to deduce therefrom thevariation in the distance between the cable anchors A and B.

[0134] Other variants can be considered of the device used to measurethe distance variation between the cable anchors A and B. Thus using anoptonumerical system enables the evolution of the distance between atarget and the instrument to be determined by means of digital imagingprocessing in real time.

1. A method of tensioning a multiple strand cable (12) in which saidstrands (13, 13A) are installed one after the other between two cableanchors (A, B) fastened to the structure, the method consisting of:pulling on one end of a strand (13A) from one of the cable anchors (A)with the other end fixed to the other cable anchor (B), measuringcontinuously the value of the tension in the strand (13A), andcontinuously testing a condition for ending tensioning for the strand(13A), said condition employing an expression that is a function of apredetermined parameter (Δd), which method is characterized in that saidpredetermined parameter is the variation (Δd) in the distance betweensaid cable anchors (A, B).
 2. A tensioning method according to claim 1,characterized in that it consists of: a) determining the theoreticalvalue of the zero tension length (L_(th)) of the cable (12) as afunction of: the total number (n) of strands (13) of the cable (12), theaxial stiffness (Ea) and the weight per unit length (q_(t)) of each ofthe strands of the cable (12), the theoretical position ({right arrowover (X)}A₀, {right arrow over (X)}B₀) of the cable anchors (A, B) asdefined by the drawings of the structure, the tension (T_(pr)) in thecable (12) and the displacements ({right arrow over (μ)}A_(pr), {rightarrow over (μ)}B_(pr)) of the cable anchors predicted by the designcomputations for the structure for a predetermined reference phaseoccurring after tensioning the cable (12), b) evaluating the initialdisplacements ({right arrow over (μ)}_(A1), {right arrow over (μ)}_(B1))of the cable anchors (A, B) immediately before installing the firststrand of the cable (12), c) during the tensioning of each strand (13A)of the cable (12): measuring continuously said distance variation (Δd)from the step b), executing a computation loop to test continuously thecondition for ending tensioning the strand (13A), using said expressionwhich is a function of said predetermined parameter (Δd), and d) lockingthe strand (13A) being tensioned to the cable anchor (A) as soon as thecondition for ending tensioning of the strand (12, 13A) is satisfied. 3.A tensioning method according to claim 2, characterized in that saidexpression which is a function of said predetermined parameter definesthe stretch (Δl) remaining to be applied to the strand (13A) until thecondition for ending tensioning is satisfied.
 4. A tensioning methodaccording to claims 2 and 3, characterized in that said expression isdefined by the following parameters: i) the stiffness (Ea) and theweight per unit length (q*) of the strand (13, 13A), ii) the theoreticalzero tension length (L_(th)), iii) said initial displacements ({rightarrow over (μ)}A₁, {right arrow over (μ)}B₁), iv) the tension measuredin the strand (13, 13A), and v) said distance variation (Δd), and inthat the strand is locked when the stretch (Δl) remaining to be appliedis equal to zero.
 5. A tensioning method according to claim 4,characterized in that said expression is also defined by a value (rc)representing the insertion of the keys by which said strand (13, 13A) isanchored to its cable anchor (A).
 6. A tensioning method according toclaim 2, characterized in that said expression which is a function ofsaid predetermined parameter (Δd) defines the locking tension (T) thatsaid strand (13, 13A) must reach before it can be anchored.
 7. Atensioning method according to claims 2 and 6, characterized in thatsaid expression is defined by the following parameters: i) the stiffness(Ea) and the weight per unit length (q*) of the strand (13, 13A), ii)the theoretical zero tension length (L_(t)h), iii) said initialdisplacements ({right arrow over (μ)}A₁, {right arrow over (μ)}B₁), iv)said distance variation (Δd), and in that the strand is locked when themeasured value (V2) of the tension applied to said strand (13, 13A)becomes equal to that (T) of the tension calculated in this way.
 8. Amethod according to any of claims 1 to 7, characterized in that saidinitial displacements ({right arrow over (μ)}A₁, {right arrow over(μ)}B₁), are measured on the structure by a procedure taking account ofthe construction tolerances of said structure.
 9. A tensioning methodaccording to any of claims 1 to 7, characterized in that said initialdisplacements ({right arrow over (μ)}A₁, {right arrow over (μ)}B₁), aredetermined from the results of design computations for the structure.10. A tensioning method according to any of claims 4 to 9, characterizedin that the cable (12) includes a protective sheath (14) and the methodfurther consists of: i) determining the theoretical zero tension length(L_(th)) from the weight per unit length (q_(g)) of said sheath (14),and ii) during the computation relating to said condition for endingtensioning, increasing the weight per unit length of the strand (13A)being tensioned by a fraction (q_(g)/i) of the weight per unit length(q_(g)) of the sheath (14).
 11. A tensioning method according to any ofclaims 2 to 10, characterized in that it also consists of taking accountof the temperature (θ_(tor)) of the strand (13A) being tensioned duringstep c) in the computation relating to said condition for endingtensioning.
 12. A tensioning method according to any of claims 2 to 11,characterized in that it also consists of taking account of thetemperatures of the cables already installed on the structure (7 to 11)and of the structure itself (1 to 6) during step b) in the determinationof said initial displacements ({right arrow over (μ)}A₁, {right arrowover (μ)}B₁).